I am not sure that I understand. Do you mean, how do you stop them from claiming them on taxes? If so, the IRS will review and flag returns where more than one person has claimed children. They may require the person to amend if they had no right to claim them. As a general rule, the person who provides more than 50% of the care will be able to claim them on taxes.
You question is not clear. However, I take your question to mean that an ex-spouse wants to claim children on his/her income tax return, when you are the custodial parent and the children are otherwise your qualifying dependents.
File your tax return taking all of the deductions and credits to which you are entitled. If your ex also claims the dependent exemption, the IRS will send both of you a letter. Your response to the letter wll be your opportunity to demonstrate that you are entitled to claim the depedent deductions and credits.